第39回統計的機械学習セミナー / The 39th Statistical Machine Learning Seminar

Date&Time
2017年10月3日(火)
/ 3 October, 2017 (Tue) 14:00 - 16:00

Admission Free,No Booking Necessary

Place
統計数理研究所 セミナー室5 (D313 & D314)
/ Seminar room 5 (D313 & D314) @ The Institute of Statistical Mathematics
区切り線
Speaker 1
Satoshi Ito (The Institute of Statistical Mathematics, Tokyo)
Title
Nonlinear Integer Programming Formulations for Calculating Clinch / Elimination Numbers in League Sports
Abstract
Some nonlinear integer programming formulations are discussed for calculating clinch and elimination statistics in league sports. The clinch (elimination) number is the minimal number of future wins (losses) needed to clinch (to be eliminated from) a specified place in the current season. We confine ourselves in this talk to the cases where ties are possible and the winning percentage is used to determine team standings. We may also assume the existence of a predefined tie-breaking procedure, without playing additional games, when one or more teams end the season in a tie. The resulting problems have been difficult to solve so far, but are now getting tractable thanks to the recent advancement in nonlinear MIP technology.
区切り線
Speaker 2
Stefan Vigerske (GAMS, Zuse Institute Berlin)
Title
MINLP Solver Technology
Abstract
To solve mixed-integer nonlinear optimization problems (MINLP) to global optimality, a rich set of techniques is applied to find optimal solutions and prove their global optimality. Current state-of-the-art solvers for this problem type are based on spatial branch-and-bound, where the bound is computed from a linear or mixed-integer linear relaxation of the problem and branching may be applied to both integer and continuous variables. To construct the relaxation, the algebraic structure of the nonlinear functions that define the objective and constraints is analyzed. In this talk, we give a short overview on the algorithmic techniques that are employed in state-of-the-art global solvers for mixed-integer nonlinear optimization problems, in particular convexification and bound tightening approaches and primal heuristics.